Several educational devices which employ the concept of color-coding a problem with a related answer have been proposed, however these educational aids are handicapped by a number of disadvantages that prevent them from being entirely successful or readily acceptable to students and educators.
U.S. Pat. No. 1,244,000 issued Oct. 23, 1917 to H. Soltoft and U.S. Pat. No. 4,176,472 issued Dec. 4, 1979 to M. T. Devanney use color-coding to reinforce the concept of number valuation. Both of these educational devices, however, are directed only to teaching the value and use of numbers and can be conveniently employed by only one user at any one time. Also, no independent answer verification is provided to the user to confirm a correct response; only the matching of colors provides this confirmation. Additionally, the former provides that a combination of colors be used for a single response in some instances (i.e. for the response of "10", the integer "1" and the integer "0" are lined in different colors), thus leading to additional printing costs for the elements containing these responses and confusion on the part of the user. The latter requires that a bulky frame be used to support and display the educational device and is only designed to incorporate the integers 0 through 10.
A second group of patents, typified by U.S. Pat. No. 1,450,395 issued Apr. 3, 1923 and U.S. Pat. No. 1,696,988 issued Jan. 1, 1929, both to N. Y. Troidl, and U.S. Pat. No. 3,864,850 issued Feb. 11, 1975 to A. P. Helmecke, employ color-coding of arithmetical problems and related answers. With these educational devices, however, problem and answer components must be physically placed side by side in order for the user to verify that his or her response is correct and even then, only the matching of colors provides this confirmation (again, no independent answer verification is provided to the user). Also, because bulky frames or similar supports limit the capacity of these teaching devices, they are unable to conveniently contain a sufficient number of integers to display all possible problem and answer combinations. The nature of these educational devices also renders them suitable for only one user at a time. Also, with these devices, it is necessary for every answer to occupy a separate component of the apparatus; with the first two patents, this consists of a single answer affixed to one face of a cube or card and with the latter, this consists of a single answer per card. Having every individual answer occupy a separate component of the apparatus reduces the device's ability to conveniently accommodate an expanded array of answers. Also, two of these patents, U.S. Pat. No. 1,450,395 and U.S. Pat. No. 3,864,850 use more than one color for different components of a single equation, thus leading to additional printing costs for the elements bearing the equation components and generally reducing the effectiveness of the use of color as a mnemonic device. The latter also employs a combination of two colors for a single response, i.e. each integer of a two digit response is lined in a different color.
Educational devices which are limited to the teaching of multiplication through the use of color-coded problems and related answers are typically illustrated by U.S. Pat. No. 239,385 issued Mar. 29, 1881 to J. E. Irwin and U.S. Pat. No. 1,466,501 issued Aug. 28, 1923 to A. A. Gamble. Both of these devices share several of the disadvantages cited above, namely the absence of an independent answer verification, the requirement that problem and answer components by physically placed side by side to verify response, and the convenient use of the apparatus by only one user at a time. Also, with these patents, every answer must be contained on a separate component of the apparatus and neither of these devices provide for the inclusion of the singular integer 0. An additional disadvantage not previously mentioned, for both of these devices, is that equations must be broken into three components consisting of the multiplier, the multiplicand and the product, rather than two components consisting of the multiplier and the multiplicand combined and the product. Having three separate components requires that the educational device employ more elements than is necessary to effectively convey its concept. In addition, U.S. Pat. No. 1,466,501 is contained in a framework that limits its physical capacity and renders it unable to provide for all possible combinations of multiplier and multiplicand. This patent also employs more than one color for different components of any single equation and also uses a combination of two colors, in some instances, for multiple integers of a single response, both of which can lead to confusion on the part of the user.
Other educational devices, believed to be more closely related to my invention are typically illustrated by U.S. Pat. No. 1,836,851 issued Dec. 15, 1931 to G. W. Kidd, U.S. Pat. No. 2,901,839 issued Sept. 1, 1959 to D. E. Huff, and U.S. Pat. No. 3,061,947 issued Nov. 6, 1962 to D. W. Faudree. All of these devices, however, suffer from the disadvantage of using more than one color for different parts of a single equation. U.S. Pat. No. 2,901,839, in fact, even color codes the same specific answer with different colors in different instances, i.e. when multiplying 7 times 8, the response of "56" is coded in black and when multiplying 8 times 7, the response of "56" is coded in orange, thus causing confusion for the user and reducing the effectiveness of the use of color as a mnemonic device. This patent also displays solutions on the face of the apparatus where the problem appears, thus eliminating the device's ability to solicit an answer from the user. U.S. Pat. No. 3,061,947 uses a combination of colors for multiple integers in certain single responses, this also providing confusion to the user and reducing the effectiveness of the teaching device. U.S. Pat. No. 1,836,851 also has a number of disadvantages mentioned for patents previously discussed, that is the requirement that problem and answer components be physically placed side by side to confirm a user's response, the absence of independent answer verification, and the convenient use of the apparatus by only one user at a time. Also, in U.S. Pat. No. 1,836,851, equations must be broken into three components, rather than two, and only the integers 1 through 5 are incorporated as possible problem components.